Optimal iterative learning control design with trial-varying initial conditions

Designing an optimal iterative learning control is a huge challenge for linear and nonlinear dynamic systems. For such complex systems, standard Norm optimal iterative learning control (NOILC) is an important consideration. This paper presents a novel NOILC error convergence technique for a discrete-time method. The primary effort of the controller is to converge the error efficiently and quickly in an optimally successful way. A new iterative learning algorithm based on feedback based on reliability against input disruption was proposed in this paper. The illustration of the simulations authenticates the process suggested. The numerical example simulated on MATLAB@2019 and the mollified results affirm the validation of the designed algorithm.

In this paper, we study MIMO Iterative Learning Control (ILC) and its robustness against model uncertainty. Although it is argued that, so-called, norm optimal ILC controllers have some inherent robustness, not many results are available that can make quantitative statements about the allowable model uncertainty. In this paper, we derive sufficient conditions for robust convergence of the ILC algorithm in presence of an uncertain system with an additive uncertainty bound. These conditions are applied to norm optimal ILC, resulting in guidelines for robust controller design. Theoretical results are illustrated by simulations.

Resource-efficient ILC for LTI/LTV systems through LQ tracking and stable inversion: Enabling large feedforward tasks on a position-dependent printer

The tracking performance of two iterative learning control algorithms is compared to that, which can be achieved by an optimal feedback controller. P-type iterative Learning Control in parallel with a proportional feedback controller is compared with norm-optimal iterative learning control, then both ILC systems are compared with the performance achieved by an optimal feedback controller. Considering that the ILC plus proportional controller requires no prior modelling of the plant and minimal adjustment of gains, the tracking performance in terms of mean squared error (mse) per iteration can be reduced by two orders of magnitude further than can be achieved with the optimal feedback controller. However, the Norm-Optimal ILC improves upon this performance by reducing the mse by an extra order of magnitude. The experimental results are derived from tests performed on a gantry robot.

Iterative learning control (ILC) is applicable to systems that are required to repeatedly track a desired trajectory of finite duration. Norm-optimal ILC can be characterised as a combined feedforward and feedback learning approach, where the tracking error from the previous trial and the tracking error of the current trial are employed to reduce the tracking error from trial to trial. In this paper, a high speed rack feeder typically used in automated warehouses is considered, which represents a flexible beam structure with a vertically moving mass. Due to kinematic constraints such as a maximum velocity and a maximum acceleration, standard ILC is not applicable if the desired trajectory violates these constraints. One possible solution would be an offline trajectory planning subject to the given kinematic constraints. This paper, however, addresses modifications of the ILC algorithm itself to cope with infeasible trajectories. Two alternative algorithms are given for this purpose and compared with each other in experiments on a test rig that replicates the dynamics of a high speed rack feeder.

The optimal solution from the lifted system design methods presented by Tousain (2001) has many advantages over classic iterative learning control (ILC) design methods, with one drawback: the ILC solution has to be recalculated for every trajectory of a different length. This paper shows that it is very well possible to avoid this by expressing the solution for the lifted system ILC as a finite time function of the plant parameters. This solution will be referred to as an extrapolated solution since the solution can be used for a trajectory of any length without recalculating the solution. This low order extrapolated solution has been compared to a high order lifted system optimal control (Q-)ILC solution in the application to an industrial grade wafer stage, showing the value of this extrapolated solution.

In this paper, a modified learning gain for Iterative Learning Control (ILC) approach is proposed for linear Multi-Input-Multi-Output repetitive systems. The control law synthesis is based on the resolution of a quadratic criterion which minimizes the error between the setpoint references and the system outputs at each iteration for each trial. The resolution of the control problem leads to a new gain which avoids matricial inversion problems appeared with classical ILC algorithms such as direct model inversion (I-ILC) and optimal ILC (Q-ILC). The modified type ILC approach improves the learning convergence significantly compared to I-ILC and Q-ILC algorithms. Furthermore, a sufficient and necessary stability condition and convergence properties are established. Simulations with a MIMO Mass-spring damper system show the effectiveness of the proposed method.

In this paper, an optimal iterative learning control (ILC) approach is proposed for a class of repetitive non-minimum phase (NMP) systems. The control law synthesis is based on the resolution of a quadratic criterion which minimises the errors between the setpoint references and the system outputs at each iteration for each trial. The resolution of the control problem uses a new gain which avoids matricial inversion problems appearing in classical ILC algorithms such as direct model inversion (I-ILC) and optimal ILC (Q-ILC). The new optimal ILC approach improves the learning convergence significantly compared to the previously mentioned algorithms. Furthermore, sufficient and necessary stability conditions are established with convergence properties. The effectiveness of the proposed method is proved by simulations with an NMP mass-spring damper system.

Iterative learning control design for linear discrete-time systems with multiple high-order internal models

Optimal Iterative Learning Control for Batch Processes Based on Linear Time-varying Perturbation Model

Iterative Learning Control of a Left Ventricular Assist Device

The injection stretch blow moulding (ISBM) process is widely used to manufacture plastic bottles for the beverage and consumer goods industry. The majority of the production processes are open-loop systems, often suffering from high raw material and energy waste. In this paper, a heuristic based norm-optimal terminal iterative learning control (ILC) method is proposed to control the preform temperature profiles in the reheating process. The reheating process is a batch process, and ILC can achieve improved tracking performance in a fixed time interval. The terminal ILC (TILC) is a useful strategy when only the terminal temperature profile can be measured in a batch process like the preform reheating in ISBM. To balance the control performance and energy cost, a norm-optimal method is applied, leading to a proposal of the new norm-optimal TILC method in this paper. Heuristic methods including the swarm optimisation (PSO), differential evolution (DE) and teaching-learning based optimization (TLBO) are used to calculate the sequence of norm-optimal control inputs for this non-linear batch process. Simulation results confirm the efficacy of the proposed control strategy.

While iterative learning control (ILC) and repetitive control (RC) have much ground in common, they fundamentally differ in the initial conditions at each repetition. This difference has lead to distinct analysis techniques, hereby clouding the interrelations between both control strategies. To facilitate the transfer of results, this paper presents a unified approach to ILC and RC. Both control problems are formulated in the trial domain using so-called system lifting. For a given system, the corresponding ILC and RC trial-domain models differ, and a thorough system theoretic analysis and comparison of these models is performed. To illustrate the value of a unified formulation of ILC and RC, the analysis of the most commonly used ILC and RC structures is harmonized. This analysis reveals central differences and similarities between various stability, monotonic convergence and steady-state performance conditions.

The repetitive processing and large quantity of single product represented by 3C products are urgently needed. However, for current processing operations, previous processing data have not been used in the optimization of control input. In order to utilize previous processing data to facilitate the next process and avoid adverse effects caused by repetitive disturbance and noise, the idea of iterative learning was introduced to improve the accuracy of machining. On the control level, since it is difficult to obtain high accuracy by traditional feedback control when faced with complex trajectories, an open-loop iterative learning controller and a position loop feedback controller were introduced, which worked fast with good convergence effects. Aiming at reducing the influence of accidental error, step type iterative learning was put forward. The iteration mechanism was stopped when the accuracy converged to the allowable range so as to reduce computational complexity, store the current iterative part of the control input, and make constant value compensation. However, in simulation and experiment, it was found that after superposition of the iterative learning controller, the phenomenon of partial divergence of the system tracking error occurred. Therefore, the speed and acceleration characteristics of input trajectories in time domain and frequency domain were analyzed. High-frequency noise was introduced in frequency domain, which was found to be the cause of the abovementioned phenomenon, and high-frequency components were filtered to solve the problem. To further improve the accuracy of convergence and avoid filtering effective high-frequency information in some area, a switchable filter based on the analysis of the frequency characteristics of input trajectory was proposed. Through SIMULINK simulation and dSPACE experimental verification, it was proved that the iterative learning controller of modifying controlled quantity and filter based iterative learning control method are effective.

In this paper, we consider the norm-optimal iterative learning control (NO-ILC) framework and study its robust monotonic convergence (RMC) against model uncertainties in single-input-single-output linear time-invariant systems. Modeling errors in general degrade the convergence performance of NO-ILC, and hence ensuring RMC against model uncertainties is important. Although the robustness of NO-ILC has been studied in the literature, determining the allowable range of modeling errors for a given NO-ILC design is still an open research question. To fill this gap, a frequency-domain analysis with a multiplicity formulation of model uncertainty is developed in this paper to quantify and visualize the allowable modeling errors. Compared with the traditional formulation, the proposed new uncertainty formulation provides a less conservative representation of the allowable model uncertainty range by taking additional phase information into account and thus allows for a more complete evaluation of the robustness of NO-ILC. The analysis also clarifies how the RMC region changes as a function of NO-ILC weighting parameters and therefore can be used as a frequency-domain design tool to achieve RMC for given model uncertainties. Simulation examples are given to confirm the theoretical conclusions and demonstrate the utility of the developed analysis.